A062408 Numbers k such that floor(Pi*k) is prime.

1, 10, 12, 14, 15, 17, 19, 31, 33, 35, 36, 42, 50, 52, 57, 61, 63, 71, 73, 77, 80, 82, 84, 98, 99, 101, 117, 119, 122, 124, 138, 140, 143, 147, 159, 166, 182, 187, 189, 201, 206, 208, 210, 220, 226, 229, 241, 245, 254, 262, 264, 273, 275, 289, 290, 296, 308, 311

Offset: 0

Author

Jason Earls, Jul 08 2001

Keywords

• nonn

Comments

Chua, Park, & Smith prove a general result that implies that, for any m, there is a constant C(m) such that a(n+m) - a(n) < C(m) infinitely often. - Charles R Greathouse IV, Jun 30 2022

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000
• Lynn Chua, Soohyun Park, and Geoffrey D. Smith, Bounded gaps between primes in special sequences, Proceedings of the AMS, Volume 143, Number 11 (November 2015), pp. 4597-4611.

Crossrefs

Cf. A022844, A067559.

Programs

Mathematica

Select[Range[1, 400], PrimeQ[Floor[Pi #]] &] (* Bruno Berselli, Sep 30 2012 *)

PARI

je=[]; for(n=0,1000, if(isprime(floor(Pi*n)),je=concat(je,n),)); je

PARI

{ default(realprecision, 50); n=-1; for (m=1, 10^5, if (isprime(floor(Pi*m)), write("b062408.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 07 2009